Images and Geometry

Leader of the Group: Dr. Renjie Chen

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Vision and Research Strategy

As its core mission, computer graphics endeavors to deliver natural-looking and convincing graphic contents, such as images, videos and 3D models for various applications, including design, entertainment, education, simulation, etc. In many cases, “natural-looking” can be interpreted as low distortion with respect to some reference. Depending on the application, the distortion can be measured as the amount of feature stretching, non-feature noise, change of scale, self-overlapping, and so on. As distortions can largely affect human perception of the contents, we want to generate images and shapes with no distortion or controlled amount of distortions. The objective of this research group is to design algorithms for various image and geometry applications, such that the results will be of low distortion and high-quality.



Research Areas and Achievements

Geometric Modeling

A basic requirement for shape deformation is the results should not have any self-overlapping, i.e., the map should be bijective. Even in 2D, there’s currently no answer to the following question. Given a triangular mesh, is it possible to map it to a new mesh with an arbitrary new boundary? We gave an answer in an algorithmic approach using the minimal area surfaces. Besides bijectivity, more general distortion measures, such as conformality, area-preserving, rigidity, quasiconformal factor, etc., are used in different applications. In the context of shape interpolation, we propose to interpolate the continuous metrics of the shapes and then use conformal maps to flatten the interpolated metric. Our continuous mathematical formulation provides appealing properties such as existence and uniqueness of the solution, smoothness in space and time domains, and most importantly, the bounded amount of conformal distortion. The space of exact conformal maps is usually quite limited. As a generalization of conformal maps, harmonic maps are extensively used in geometry processing applications to produce visually appealing deformations. We proposed to use harmonic mapping for shape deformation such that we can control the distortion of the whole shape by focusing on the boundary map, where the problem is of lower dimension and hence easier to solve.


Image Retargeting

Image retargeting is the process of rearranging the content in a given image to form a new image that more conforms to the user’s requirements. We developed a method for resizing images in a content-aware manner. By constraining the important parts of the image to have less or no stretch and hiding the distortion in less important or more flat regions, we generate images that are perceptually less distorted. The content-aware image resizing methods can be used for other general image applications. We show how these methods can be employed to change the compositions of photographs, i.e. how salient objects and features are positioned within the image frame. We further use optimization tool to improve the composition of photographs taken by amateurs.


Glasses free 3D display

Over the last few years, a new generation of displays has started to emerge: compressive light field displays. These types of displays support unprecedented image resolution and 3D capabilities. Despite the efficiency gains made by compressive displays, these displays still have limited display bandwidth: they are unable to present glasses-free imagery over a wide field of view. We explore the combination of compressive light field displays and head tracking by steering a small instantaneous field of view dynamically into the direction of multiple tracked observers. We show the perceived field of view and the image quality of the display can be significantly improved.